Example:

Suppose you work for an ice-cream company. The company wants to create a new flavor ice-cream and wants to determine if the flavor should be chocolate or vanilla. What is the smallest sample size the company can collect to estimate the proportion (percentage) of all people who prefer chocolate over vanilla. Assume a confidence interval (CI) of 90% and an allowable margin of error (E) of .03 and a known standard deviation of 10.4.

ANSWER:

This question is asking us to calculate the sample size “n”.

We are being told that the margin of error E is .03. The problem is also asking for a 90% CI.

HOW TO GET the Critical Values for 90% CI

n = [zc^2  * p  * (1 – p) ] / E^2

At this point, you might notice that we need “p” for the formula. Recall that “p” is the proportion of people who prefer chocolate (in this example).

However,  in this case, and in many cases, we do not know p.

If “p” is not known and is not given, always use p = .5.

n = [zc^2  * p  * (1 – p) ] / E^2

n = [1.645^2  * .5  * (1 – .5) ] / (.03)^2

n = [1.645^2  * .5  * (1 – .5) ] / (.03)^2

n = [2.71  * .5  * (1 – .5) ] / (.03)^2

n = [2.71  * .5  * (.5) ] / (.03)^2

n = [.678 ] / (.03)^2

n = .678 / .0009

n = 753.3

NOTICE:

You can estimate the sample size using

n = 1/E^2

To do this, you will need to calculate “E” using the correct formula and assuming you have all the information that you need.

HOW TO Calculate E for Proportions and a Given Confidence Interval

 

 

n = .68/